This is the story of John Lennon. We see him as a teenager, being raised by his aunt and uncle. He hasn't seen his mom since he was very young, but he doesn't know why he isn't living with her (didn't he ever think of asking his aunt?). Early in the movie, his friend shows him where his mother lives - just around the corner, it seems. So he gets reacquainted with his mother, and she turns him on to rock and roll. We also see he is a bit of a troublemaker, skipping school and stealing records with a friend.
The first half hour or so really bored me. There isn't much story or plot to speak of. We are just watching Lennon be a troubled youngster. At some point, his mother teaches him to play the banjo. Then he decides he wants to be a rock star and he gets a band together. We see him meet Paul McCartney and George Harrison. Here the movie gets interesting. We see him try to get the band to write originals rather than playing cover songs. But the movie kind of skims over the details.
I think the bigger of a John Lennon fan you are, the more you will enjoy the movie.